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Validating Software Metrics: A Spectrum of Philosophies
Andrew Meneely
Ben Smith
Laurie Williams
North Carolina State University
(apmeneel, bhsmith3, lawilli3)@ncsu.edu
Abstract
Context: Researchers proposing a new metric have the burden of proof to demonstrate to the research
community that the metric is acceptable in its intended use. This burden of proof is provided through the multi-
faceted, scientific, and objective process of software metrics validation. Over the last 40 years, however,
researchers have debated what constitutes a “valid” metric.
Aim: The debate over what constitutes a valid metric centers on software metrics validation criteria. The
objective of this paper is to guide researchers in making sound contributions to the field of software engineering
metrics by providing a practical summary of the metrics validation criteria found in the academic literature.
Method: We conducted a systematic literature review that began with 2,288 papers and ultimately focused on
20 papers. After extracting 47 unique validation criteria from these 20 papers, we performed a comparative
analysis to explore the relationships amongst the criteria.
Results: Our 47 validation criteria represent a diverse view of what constitutes a valid metric. We present an
analysis of the criteria’s categorization, relationships, advantages, and philosophical motivations behind the
validation criteria. We then present a step-by-step process for selecting appropriate metrics validation criteria
based on a metric’s intended use.
Conclusions: The diversity of motivations and philosophies behind the 47 validation criteria indicates that
metrics validation is complex. Researchers proposing new metrics should consider the applicability of the
validation criteria in terms of our categorization and analysis. Rather than arbitrarily choosing validation criteria
for each metric, researchers should choose criteria that can confirm that the metric is appropriate for its intended
use by inspecting the advantages that different criteria provide. We conclude that metrics validation criteria
provide answers to questions that researchers have about the merits and limitations of a metric.
Keywords: software metrics, validation criterion, systematic literature review
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1. Introduction
Practitioners and researchers alike use software metrics to both improve and understand software products and
the software development processes. The field of software metrics has a variety of applications including quality
assessment, prediction, task planning, and research. Researchers proposing a new metric have the burden of
proof to demonstrate to the research community that the metric is truly representative of the attribute it is
intended to represent.
But how do we, as a community, ensure that a metric is suitable and acceptable for its intended purpose?
Without some formal system of rules for the determining the merits of a metric, the software engineering
community could find itself flooded with metrics that lend no understanding to the state of the art. This system
of rules for ensuring the worthiness of a metric is known as software metrics validation, and software
engineering researchers have debated what constitutes validation for almost half a century.
The community has not yet reached a consensus on this system of rules. Instead, software metrics researchers
have often been proposing their own, specialized means of validation. This ad hoc approach to validation leads
to results that cannot be generalized and to contributions that are not stated in a manner consistent with a
standard form of metric validation.
Before we look at where metric validation must go, we must look at where it has been. The metrics validation
community has likely not reached a consensus because no researcher has provided a "proper discussion of
relationships among the different approaches [to metric validation]" (Kitchenham, Pfleeger et al. 1995). The
objective of this paper is to guide researchers in making sound contributions to the field of software engineering
metrics by providing a practical summary of the metrics validation criteria found in the academic literature. We
performed a systematic literature review, beginning with 2,288 potential peer-reviewed publications and
ultimately focused on 20 publications that propose or indicate software metrics validation criteria. Our review is
a useful guide for two audiences: 1) metrics researchers: software engineering researchers who propose, use,
and validate new metrics; and 2) metric validation researchers: software engineering researchers seeking to
propose methodologies, criteria, or frameworks for validating metrics.
Metrics researchers will want to use this review as:
• A reference guide. We have compiled a list of the unique criteria presented in the literature with definitions
and examples. Additionally, metrics researchers can see where authors discuss the same criteria but with
different vocabulary.
• A source for threats to metric validity. Metrics researchers can consult our survey to enumerate the issues
a given metric may encounter. Furthermore, this source acts as a guide on issues where the community
disagrees or published criteria contradict each other.
• A big picture. We present a hierarchical relationship among the criteria that can be used to gain an
understanding of how a given criterion relates to the "big picture" of software metric validation. Our
analysis of the philosophical motivations behind a validation criterion is helpful for understanding not only
the criteria themselves, but the “spirit” of the criteria.
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• Inspiration. The criteria that have been proposed can act as a set of guidelines to help inspire a new way of
thinking about metrics. Our comparative analysis of the criteria introduces underlying, tacit concepts that all
researchers should be aware of when considering new metrics.
Software metrics validation researchers will want to use this review as:
• A roadmap for current criteria. We provide the validation criteria that researchers can use to view how
their proposals fit into the overall body of work on metric validation.
• A call for discussion. In analyzing the validation criteria in the literature, we have summarized the
discussion surrounding metric validation. We have found that this discussion has not concluded and wish to
re-invigorate the discussion in the research community to help reach a consensus on what is meant by
metric validity.
• A direction for a standard. Understanding the categorization and the motivation of the validation criteria
assists the metrics validation community in deciding on a standard set of criteria for validating a metric.
• A guide for future criteria. The hierarchical relationship we discovered when comparing the criteria can
serve as a tool for generating new metrics validation criteria. Areas of metric validation are missing in the
overall hierarchy, and new criteria could be proposed that address these areas.
This paper is organized as follows. In Section 2, we present the terms specific to this review and their
definitions. Next, in Section 3 we present the process we used to conduct the review. We present the extracted
criteria in Section 4 and the mapping of their relationships in Section 5. Section 6 outlines the philosophies of
the two opposing motivations behind the criteria. In Section 7, we describe how to use a metric’s intended use
to choose the appropriate validation criteria. Finally, Section 8 concludes.
2. Terms and Definitions
During our review, we found many different usages and definitions for the same words, so we define our usage
of these words in Section 2.1. Next, we define examples of metrics that we refer to throughout the paper in
Section 2.2.
2.1 Metric Terminology
• Attribute: The specific characteristic of the entity being measured (IEEE 1990). For example, the attribute
for a Lines of Code metric is "size".
o Internal attribute: Attributes that the product itself exhibits. For example, the size of code
(ISO/IEC 1991) is an internal attribute. (Fenton and Kitchenham 1991).
o External attribute: Attributes that are dependent on the behavior of the system. For example, the
reliability of a system is an external attribute (ISO/IEC 1991).
• Component: One of the parts that make up a software system. A component may be hardware or software
and may be subdivided into other components (IEEE 1990).
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• Failure: an event in which a system or system component does not perform a required function within
specified limits (ISO/IEC 1991).
• Fault: an incorrect step, process, or data definition in a computer program (ISO/IEC 1991).
• Metric: a "quantitative scale and method which can be used to determine the value a feature takes for a
specific software product" (IEEE 1990). Fenton (Fenton and Neil 2000), (Fenton 1994) explains that
essentially any software metric is an attempt to measure or predict some attribute (internal or external) of
some product, process, or resource. Fenton (Fenton and Kitchenham 1991) points out that metric has been
used as:
o a number derived from a product, process or resource;
o a scale of measurement
o an identifiable attribute (see above).
Also, a metric measures the degree to which a system, component or process possesses a given
attribute (see above) (IEEE 1990). An internal metric measures an internal attribute, and an external
metric measures an external attribute.
• Quality Factor: an attribute of software that contributes to the degree to which software possesses a
desired combination of characteristics (Schneidewind 1992).
• Statistical correlation: we use the term "statistical correlation" in the broad sense of one variable "co-
relating" with another, not to be confused with the correlation coefficients that are specific statistical tests
used to estimate the correlation between two variables.
• Validation: the ISO/IEC of definition of validation is "confirmation, through the provision of objective
evidence, that the requirements for a specific intended use or application have been fulfilled" (ISO/IEC
1991).
2.2 Examples
In our discussions throughout this paper, we use five examples of metrics to illustrate concepts found in the
criteria. We list the referenced definitions for these metrics here:
• Lines of Code (LOC) metric: the general notion of counting the number of lines of source code in a
program, without prescribing a specific counting standard.
• Cyclomatic Number: McCabe's cyclomatic complexity (McCabe 1976), which is based on the number of
edges, nodes, and components in a program flow graph.
• Code Churn: a measure of how much a unit of code has changed over a period of time, usually measured
by the number of lines of code changed at each revision in the version control system (Elbaum and Munson
1998).
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• Static Analyzer: a tool that performs automated static analysis on source or binary code, such as FindBugs
(N. Ayewah, D Hovemeyer et al. 2008). An automated static analysis tool is a program that analyzes
another program's source code and reveals possible faults in the form of "warnings".
• Code Coverage: the percentage of a structural entity that is executed by a given test set. For example
statement coverage is the percentage of statements executed by the test suite.
3. Methodology and Process
Kitchenham recommends a procedure for conducting systematic literature reviews (Kitchenham 2004), which
we follow for this review. One goal of a systematic literature review is "to provide a framework/background in
order to appropriately position new research activities" (Kitchenham 2004). The following sub-sections focus on
the bottom two tiers: gathering the literature and analyzing the literature. The process is broken down into two
parts: planning the review (Section 3.1) and conducting the review (Section 3.2).
3.1 Planning the Review
To begin our systematic literature review, we conducted a preliminary mapping study to identify our research
objective, based on Kitchenham’s systematic review process (Kitchenham 2004). As a result of this mapping
study, the objective of this paper is to guide researchers in making sound contributions to the field of software
engineering metrics by providing a practical summary of the metrics validation criteria found in the academic
literature.
Kitchenham et al. (Kitchenham 2010) also conducted a preliminary mapping study in the field of software
metrics. The Kitchenmham study focuses on influential metrics papers, while our study focuses on metric
validation. Specifically, the Kitchenham study identifies the most influential papers in the software metrics
literature by analyzing their citation counts. We focused on extracting metrics validation criteria from the
literature to summarize and analyze the existing literature.
The second step for planning a systematic literature review is to develop the search strategy, as a part of
developing the review protocol (Kitchenham 2004). As recommended in Brereton, et al (Brereton, Kitchenham
et al. 2007), we used the following search engines to conduct our review:
Google Scholar (http://scholar.google.com) CiteSeerX (http://citeseerx.ist.psu.edu/)
IEEExplore (http://ieeexplore.ieee.org) ACM Portal (http://portal.acm.org/portal.cfm)
After narrowing our research objective to focus on the criteria for validating metrics, we decided on the
following queries:
• software AND engineering AND metrics
• software AND metrics AND validation
• software AND metrics AND evaluation
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These search criteria capture a wide range of publications, so an overwhelming number of results were obtained
with each search. Since reviewing all of the results was infeasible, we developed a stopping heuristic. We used
our searches using the following method:
1. For both of the search strings, run the search on all four search engines.
2. Record the bibliographic information for any source not previously recorded that appeared to be about
the validation (or evaluation) of software engineering metrics. This step was mostly based on title and
type of publication.
3. Continue through the search results until reaching 10 consecutive, irrelevant results. Since the search
engines we used rank the results by relevance, we found this procedure to be effective at producing
useful results. In most cases, the density of relevant titles steadily decreased as we examined each
source.
4. Otherwise, continue to the next set of 10 results (step 3).
We created the form shown in Figure 1 to assess the quality of our primary sources and identify sources that fit
our research objective.
Question Answer 1. Are there clearly identifiable metrics validation criteria?
• Does the paper contain one or more criteria that can be extracted? • Is this paper an examination of what should be required to make a
software engineering metric valid? • Does this paper exhibit scientific objectiveness, or is it a "position
paper"? If the paper is a position paper, reject it.
Yes/No
2. If the answer to 1 is No, then why should this paper be excluded from the study? List reasons.
3. What are the metrics validation criteria or groups of criteria this paper describes?
• Summarize each criterion into a single bullet point. • What is the motivation for this criterion? • Is this a single criterion, or a group of criteria? • Do the authors indicate this criterion as being necessary for
validation or a desirable property?
List the criteria.
4. How is this criteria related to other criteria? • List the related criterion and its source. • Explain the rationale for the relationship
o Establish why these criteria are related. o Establish that these criteria indeed are indeed opposing, or
the same. o If these criteria conflict, do these criteria just oppose each
other, or are they truly mutually exclusive? o If these criteria are similar, are they synonyms or is there a
strong enough difference in their definition to warrant a new criterion?
List the criterion,
source, and explanation
Figure 1: Primary Source Full-Text Review Form.
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3.2 Conducting the Initial Search
The initial search consisted of a “first pass” (Section 3.2.1) through the titles, then a “second pass” (Section
3.2.2) through the abstracts of the given titles. The “third pass” was through the full texts of the chosen sources
(Section 3.2.3).
3.2.1 First Pass: Authors and Titles
In the first pass through the search results, we were as inclusive as possible because we did not read abstracts;
we tracked only titles and authors. The procedure resulted in the data presented in Table 1. The total results
column in Table 1 comes from the search engine's self-reported total number of results upon executing the
query. The reviewed results column comes from executing the procedure in Section 3.1. The researchers are
given code names: here, the first author is Researcher A and the second author is Researcher B. For example,
Researcher B searched IEEExplore for "software AND metrics AND evaluation" and found a total of 1,836,783
results. Researcher B iterated through each set of 10 results and collected the relevant titles and authors for these
sources. Then, after 90 sources, the researcher saw a set of 10 results (numbers 90-100) with no relevant titles,
and the researcher stopped.
Table 1: Search engines, queries, and results for the first pass.
Index / Search Engine
Search String (Query) Total Results
Reviewed Results Researcher
Google Scholar
software AND engineering AND metrics 125,000 270 B
IEEExplore software AND engineering AND metrics 1,492 125 B
CiteSeerX software AND engineering AND metrics 539,029 170 B ACM software AND engineering AND metrics 7,640 100 B
Google Scholar
software AND metrics AND validation 50,400 510 A
IEEExplore software AND metrics AND validation 223 223 A ACM software AND metrics AND validation 2,430 300 A
CiteSeerX software AND metrics AND validation 548,575 150 B Google Scholar
software AND metrics AND evaluation 118,000 150 B
IEEExplore software AND metrics AND evaluation 1,836,783 100 B CiteSeerX software AND metrics AND evaluation 26,953 90 B
ACM software AND metrics AND evaluation 6,898 100 A Total 3,263,423 2,288 A & B
Out of the 3 million sources returned by the search engines, we examined the titles of 2,288 sources. We
accepted 536 of the 2,288 sources we saw in the search of step one based on relevance of the title.
Several types of sources came up after completing the first pass of the initial search. Of the 536 sources found,
47% were conference proceedings and 38% were journal papers the remaining 15% were books, technical
reports, standards, presentations, and unknown. Since books are hard to locate, and are likely to present a review
of literature themselves, we eliminated books from our review. We also eliminated sources that did not have any
traceable bibliographic information, which only occurred in the searches of CiteSeerX. The next few phases of
the search are summarized by Figure 2.
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Figure 2: Overall view of the source-gathering procedure used in initial literature review
Next, we voted to confirm the 536 titles for relevance. As prescribed by Brereton, et al. (Brereton, Kitchenham
et al. 2007), Researcher A voted on whether the results found by Researcher B were relevant to the review, and
vice versa. Researcher A collected 176 unique titles, of which Researcher B accepted 64 (thus eliminating 112).
Researcher B collected 360 sources, of which Researcher A accepted 92 (thus eliminating 268). Thus, we
accepted a total of 156 titles from the voting confirmation to proceed to the next phase of the review.
3.2.2. Second Pass: Confirming the Abstracts.
After confirming the titles, we gathered the abstracts for the 156 titles and each researcher voted whether the
abstract was relevant or not with the revised criteria as shown in Table 2. Researcher A voted yes to 46 of 156
abstracts and Researcher B voted yes to 59 of 156 abstracts. The researchers agreed on 102 abstracts and
disagreed on 54. We held a meeting to form consensus on the 54 contested abstracts. Of the 54, we voted 40
abstracts as irrelevant and 14 as relevant. This result, combined with the other consensus obtained by both
researchers independently agreeing on the status of the abstracts resulted in 51 relevant abstracts total and 105
irrelevant abstracts.
Table 2: Second pass voting results
Voter Keep Discard Researcher A 46 110 Researcher B 59 97
Overall Consensus 51 105
The overall consensus on the abstracts, as determined above, was passed on to the Arbiter, the third author in
this paper. As shown in Table 3, the Arbiter voted on the relevance of the 156 abstracts and indicated that 38
9
were relevant and 118 were irrelevant. The Arbiter agreed with the researchers' consensus for 121 abstracts and
disagreed with the researchers on 35 abstracts. Another meeting was held to form overall consensus on the
abstracts. Out of the 35 abstracts discussed at the meeting, the full research team (consisting of Researcher A,
Researcher B, and the Arbiter) accepted 17 abstracts and rejected 18 abstracts. We accepted 44 abstracts total
(rejecting 112), and proceeded to the next phase of the review.
Table 3: Second pass voting with arbiter results
Voter Keep Discard Researchers A & B 51 105
Arbiter 38 118 Overall Consensus 44 112
3.2.3 Third Pass: Full Texts.
The next phase of the search was to vote on the full text for each of the 44 sources whose abstract the research
team agreed upon. The voting results of the full-text pass are shown in Table 4. Researcher A and Researcher B
then voted on whether the source matched the criteria for the systematic literature review by completing the
form shown in Figure 1 for each source.
In this phase, the researchers agreed on 29 full texts, and disagreed on 15. The researchers held another meeting
to discuss the full list of all 44 full texts. After forming consensus, 27 full texts were rejected, and 17 were
accepted (note: we added three sources in the follow-up search described in Section 3.3). The notes gathered
during the establishment of the chosen sources were used to develop the full list of 47 metrics validation criteria
described in Section 4.
Table 4: Full text third pass voting results
Voter Yes (Keep) No (Discard) Researcher A 17 27 Researcher B 16 28
Agreed 29 15 Overall Final Consensus 17 27
In summary, we searched a population of over 3 million sources, examined 2,288 titles, and selected 536
sources based on the relevance to our research objective. Of those 536 sources, we voted to confirm the
relevance and were left with 156 relevant titles. Those 156 titles were confirmed for their abstract content by
each researcher, and then the arbiter. We formed consensus on 44 relevant abstracts. The researchers then used
the full texts of each of the 44 sources to decide on a consensus of 17 sources that were used to construct this
review, and are listed in the next section.
3.3. Conducting the Follow-Up Search
After extracting data from the final 17 primary sources from the first search, we determined that in the interest
of thoroughness we should conduct a second search based upon the references of our sources. The 17 sources
for our study contained 548 unique references, which we used to conduct what is referred to as the "follow-up
search". The titles were easier to exclude in the follow-up review because the research questions had been more
solidly formulated, and the researchers had experience with knowing what papers were needed for the study.
10
The pass through the titles resulted in 22 publications. We then examined the abstracts for those 22 publications
and found eight relevant sources. After reviewing the full text for these eight sources, we selected three sources
that were relevant, bringing the total number papers included in our study to 20. None of the sources from the
follow-up review contained new metrics validation criteria. We did, however, find additional support for metrics
validation criteria we had already discovered.
4. Extracting the Validation Criteria
We analyzed each of the 20 sources and recorded all of the validation criteria presented by each source. After
extracting all criteria from all sources, we combined identical criteria together, resulting in a list of 47 unique
criteria.
Our intention is not to indicate to the reader that validating a metric requires the satisfaction of all 47 validation
criteria, nor that the reader can freely select which criteria apply to a specific situation. Rather, we intend the list
presented in Figure 3 to act as both (i) a reference point for this paper and for future research; and (ii) an
invitation the research community to continue the discussion of what should be required to designate a metric as
valid. Therefore, the criteria in the list are not considered to be orthogonal to each other as we further explain in
Section 6.
We first summarize the 47 criteria in Figure 3 in alphabetical order. We further synthesize the resultant criteria
in Section 5.
Figure 3: List of all 47 validation criteria found in the review
25. Monotonicity 26. Metric Reliability 27. Non-collinearity 28. Non-exploitability 29. Non-uniformity 30. Notation validity 31. Permutation validity 32. Predictability 33. Prediction system validity 34. Process or Product Relevance 35. Protocol validity 36. Rank Consistency 37. Renaming insensitivity 38. Repeatability 39. Representation condition 40. Scale validity 41. Stability 42. Theoretical validity 43. Trackability 44. Transformation invariance 45. Underlying theory validity 46. Unit validity 47. Usability
1. A priori validity 2. Actionability 3. Appropriate Continuity 4. Appropriate Granularity 5. Association 6. Attribute validity 7. Causal model validity 8. Causal relationship validity 9. Content validity 10. Construct validity 11. Constructiveness 12. Definition validity 13. Discriminative power 14. Dimensional consistency 15. Economic productivity 16. Empirical validity 17. External validity 18. Factor independence 19. Improvement validity 20. Instrument validity 21. Increasing growth validity 22. Interaction sensitivity 23. Internal consistency 24. Internal validity
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For the rest of this paper, a reference to a number with a pound sign denotes a reference to one of these criteria
(e.g. #30 refers to predictability). In Table 5 we present a matrix of the criteria by their numbers (see Figure 3),
and the originating sources.
Table 5. Matrix of criteria and their cited source
(Fen
ton
1994
)
(Kitc
henh
am, P
fleeg
er e
t al.
1995
)
(Cur
tis 1
980)
(Roc
he 1
994)
(Wey
uker
198
8)
(Jon
es 1
994)
(Sch
neid
ewin
d 19
91)
(El E
mam
200
0)
(Fen
ton
and
Nei
l 199
9)
(Bria
nd, E
mam
et a
l. 19
96)
(Bria
nd, E
mam
et a
l. 19
95)
(Hen
ders
on-S
elle
rs 1
996)
(Har
man
and
Cla
rk 2
004)
(Cav
ano
and
McC
all 1
978)
(Lin
cke
and
Low
e 20
06)
(Bak
er, B
iem
an e
t al.
1990
)
(Cou
rtney
and
Gus
tafs
on 1
993)
(Bus
h an
d Fe
nton
199
0)
(Fen
ton
and
Kitc
henh
am 1
991)
#1 X X X X #1 #2 X X #2 #3 X #3 #4 X X #4 #5 X X #5 #6 X X #6 #7 X #7 #8 X X #8 #9 X #9
#10 X #10 #11 X #11 #12 X X X X X #12 #13 X #13 #14 X X #14 #15 X #15 #16 X X #16 #17 X X X X #17 #18 X #18 #19 X #19 #20 X #20 #21 X #21 #22 X #22 #23 X #23 #24 X X #24 #25 X #25 #26 X #26 #27 X #27 #28 X #28 #29 X #29 #30 X #30 #31 X #31 #32 X X X X X X X #32 #33 X X X #33 #34 X X X #34 #35 X #35 #36 X #36 #37 X #37 #38 X X #38 #39 X X X X X X #39 #40 X X X X X #40
12
Table 5. Matrix of criteria and their cited source (F
ento
n 19
94)
(Kitc
henh
am, P
fleeg
er e
t al.
1995
)
(Cur
tis 1
980)
(Roc
he 1
994)
(Wey
uker
198
8)
(Jon
es 1
994)
(Sch
neid
ewin
d 19
91)
(El E
mam
200
0)
(Fen
ton
and
Nei
l 199
9)
(Bria
nd, E
mam
et a
l. 19
96)
(Bria
nd, E
mam
et a
l. 19
95)
(Hen
ders
on-S
elle
rs 1
996)
(Har
man
and
Cla
rk 2
004)
(Cav
ano
and
McC
all 1
978)
(Lin
cke
and
Low
e 20
06)
(Bak
er, B
iem
an e
t al.
1990
)
(Cou
rtney
and
Gus
tafs
on 1
993)
(Bus
h an
d Fe
nton
199
0)
(Fen
ton
and
Kitc
henh
am 1
991)
#41 X X X #41 #42 X X X #42 #43 X #43 #44 X #44 #45 X X X X #45 #46 X X #46 #47 X #47
In the following list, the sentence after the name, in italics, is our definition of the criterion, as combined from
each of the cited papers. Then, after the definition is a brief discussion of that specific criterion.
1. A priori validity. A metric has a priori validity if the attributes in association are specified in advance of
finding a correlation (Fenton 1994), (Courtney and Gustafson 1993), (Briand, Emam et al. 1995), (Baker,
Bieman et al. 1990). A priori validity is often referred to in the converse as a "shotgun correlation"
(Courtney and Gustafson 1993) where a correlation between a metric and a quality factor is found in a data
set, then explained post hoc. If one examines enough metrics (discarding any lack of correlation), one could
eventually find a statistically significant, yet fortuitous correlation. Instead, the authors point out that the
hypothesis of a metric's meaning ought to precede finding a correlation.
2. Actionability: A metric has actionability if it allows a software manager to make an empirically informed
decision based on the software product's status. (Fenton and Neil 2000), (Roche 1994) The metric should
reflect some property of the software in a way that enables managers to make decisions during the software
development lifecycle. Roche uses the terms "interpretative guidelines" and "recommendations for action"
when discussing the actionability of a metric. We introduce the term "actionability" as our interpretation of
the idea discussed by the authors.
3. Appropriate Continuity: A metric has appropriate continuity if the metric is defined (or undefined) for all
values according to the attribute being measured (Kitchenham, Pfleeger et al. 1995). Kitchenham et al.
phrase this criterion as "the metric should not exhibit any unexpected discontinuities". Discontinuities can
arise from fraction calculations where the denominator can be zero. For example, if one used the metric
F/LOC (faults per line of code), one would need to define F/LOC for LOC=0, since the equation is
discontinuous.
4. Appropriate Granularity. A metric has appropriate granularity if the mapping from attribute to metric is
not too finely- or coarsely-grained (Kitchenham, Pfleeger et al. 1995), (Weyuker 1988). This criterion is a
13
grouping of three of Weyuker's complexity criteria. Kitchenham et al. also discuss these three criteria, but
in terms of all metrics (not just complexity). The three criteria could be grouped as fine, medium, and
coarse granularity.
a. A metric has fine granularity if there are only finitely many programs that can achieve a given
measure. Weyuker's Property 2. For example, the cyclomatic number is not finely grained as
one can create an infinite number of programs that have the same cyclomatic number.
b. A metric has medium granularity if there are two programs that compute the same function,
but have different measures. Weyuker's Property 4. This property is based on the idea that
different programs can perform identical functionality with differing implementations and,
therefore, result in different complexities. For example, cyclomatic complexity has medium
granularity because one can write two programs that have different complexities, but still
perform the same functionality.
c. A metric has coarse granularity if two different programs can result in the same measure
Weyuker's Property 3. That is, not every measurement needs to be unique to a specific
program. The two programs can represent two different implementations altogether (not just
renamings of each other) and can still have the same complexity value.
5. Association: A metric has association validity if it has a direct, linear statistical correlation with an
external quality factor (Schneidewind 1991), (Schneidewind 1992), (Fenton 1994). We use the term
"direct" to imply that the metric is measured without the use of a model (e.g. regression). Measurement of
this criterion is typically performed by the Pearson correlation coefficient or the coefficient of
determination (e.g. R2) in a linear regression. Fenton uses the term "external correlation" when discussing
association validity. Note that Schneidewind and Fenton explicitly differentiate this term from "prediction"
validity (#32). Association validity differs from predictability in that association does not separate training
sets from test sets (e.g. using cross-validation), nor does association involve using a model.
Conventionally, statisticians use the word “association” to denote a statistical dependence between two
random variables, linear or not, and use the term “correlation” to denote a linear relationship (Rao 2007).
6. Attribute validity: A metric has attribute validity if the measurements correctly exhibit the attribute that
the metric is intending to measure (Kitchenham, Pfleeger et al. 1995), (Baker, Bieman et al. 1990).
Kitchenham's discussion of attribute validity focuses on the actual measurements of a metric. For example,
if one were measuring the attribute validity of the "psychological complexity" of code, one might poll a
group of developers and empirically evaluate their agreement.
7. Causal model validity: A metric has causal model validity if it can be used in a causal model that explains
a quality factor (Fenton and Neil 2000). If a metric can be used as a variable in a model of causality (e.g.
Bayesian Belief Networks), then more credence can be given to the metric's ability to cause changes in an
external quality factor. Note that a metric functioning as a variable within a causal model does not imply a
causal relationship, but indicates a stronger possibility of a causal relationship. We note the distinction
between causal model validity and causal relationship validity (see #8).
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8. Causal relationship validity: A metric has causal relationship validity if it has a causal relationship to an
external quality factor (Roche 1994), (Curtis 1980). Rather than having only a statistical correlation with an
external quality factor, the attribute measured by a metric must be shown to cause changes in the quality
attribute by a properly designed and controlled experiment. For example, warnings from a perfect static
analyzer that finds null dereferences could be used as a metric to predict null reference failures in a system
because executing a fault causes a failure. Causal relationship validity is different from causal model
validity (#7) because a causal model does have to dictate a relationship. Causal relationship validity is a
more specific instance of causal model validity and provides stronger evidence for the effect the metric has
on software quality.
9. Content validity: A metric has content validity if it applies "thoroughly to the entire domain of interest"
(Curtis 1980). A metric must capture the entire notion of an attribute to be considered valid. For example,
McCabe's cyclomatic complexity number might be considered content invalid in the domain of
"complexity" as it does not account for psychological complexity because obfuscating variable names does
not affect cyclomatic complexity but does affect psychological complexity. Curtis uses the term "face valid"
to refer to a metric broadly sampling a domain.
10. Construct validity: A metric has construct validity if the gathering of a metric’s measurements is suitable
for the definition of the targeted attribute. (Curtis 1980). The word “construct” in this sense refers to the
tool, instrument, or procedure used to gather measurements. Curtis refers to construct validity as when “the
operational definition yields data related to an abstract concept”. Showing that a metric does not have
construct validity means showing that a specific implementation of a metric is not valid. For example, a
program or tool to measure LOC may incorrectly count lines, and would therefore lack construct validity.
11. Constructiveness: A metric is constructive if it helps the researcher understand software quality (Cavano
and McCall 1978). For example, if a metric measures the attribute of “size”, but is not correlated with
quality (e.g. there are an equal number of high quality large components, and low quality small
components), then the metric is not constructive.
12. Definition Validity: A metric has definition validity if the metric definition is clear and unambiguous such
that its collection can be implemented in a unique, deterministic way (Lincke and Lowe 2006) (Cavano and
McCall 1978) (Roche 1994) (Bush and Fenton 1990; El Emam 2000). We use the term “deterministic”
from Lincke et al. to mean that, given a definition of a metric, the measurement made would be consistent
across all who implement the definition, implying full clarity and a lack of ambiguity. The term “unique”
implies that, given a definition and an artifact, the metric result should be unique from all other
measurements. Cavano calls this kind of definition “consistent” and “detailed”; Roche calls it “clear” and
“unambiguous”; Bush calls this a “precise” definition.
13. Discriminative Power: A metric has discriminative power if it can show a difference between high-quality
and low-quality components by examining components above/below a pre-determined critical value
(Schneidewind 1991), (Schneidewind 1992). The discriminative power criterion is used to establish sets of
metric values that should be considered “too dangerous” or “off limits”. For example, if the LOC metric has
discriminative power for number of faults with a critical value of 100, then components with over 100 lines
of code are more likely to have a dangerous number of faults than files with fewer than 100 lines of code.
15
14. Dimensional Consistency: A metric has dimensional consistency if the formulation of multiple metrics
into a composite metric is performed by a scientifically well-understood mathematical function
(Kitchenham, Pfleeger et al. 1995), (Henderson-Sellers 1996). Metrics require dimensional consistency if
they are to be used as composite measurements that consist of fundamental measures that contain different
units (e.g. person hours). For example, converting from a vector to a scalar loses vital information about the
entity. Kitchenham uses the example of multiplying the X,Y position coordinates on a Cartesian plane is
meaningless because, while we would obtain a value, we would not know what attribute is being measured.
15. Economic Productivity: A metric has economic productivity if using the metric quantifies a relationship
between cost and benefit (Jones 1994). That is, a metric is considered invalid if it does not result in saving
money in the long run. Jones stipulates that gathering and collecting a metric must not be cost-prohibitive.
Furthermore, achieving “good” scores of the metric must not also be cost-prohibitive. For example,
removing all known faults in a software system may be cost-prohibitive, even if it would improve a
“number of known faults” metric. We introduce the term "economic productivity" as an interpretation of
Jones' arguments against commonly-used metrics.
16. Empirical validity: A metric has empirical validity if experimentation and/or observation corroborates
either (i) the intended measurement of a metric; or (ii) the relationship between the metric and an external
software quality factor (Kitchenham, Pfleeger et al. 1995), (Briand, Emam et al. 1995). Empirical validation
is typically performed with statistical analysis of data obtained via experiments or project history.
17. External validity: A metric has external validity if it is related in some way (e.g. by prediction,
association or causality) with an external quality factor (El Emam 2000), (Briand, Emam et al. 1995),
(Baker, Bieman et al. 1990), (Fenton 1994). External validity is a broad category of validation criteria. For
example, if one showed that files with a high LOC is associated with having many faults, then LOC would
be considered externally valid. However, correlating LOC with another internal metric, such as code churn,
would not be considered external validation. El Emam equates the term “external” with “empirical”
validation (El Emam 2000), and we distinguish the two terms. For an in-depth discussion on the difference,
see Section 5.1.
18. Factor Independence: A metric has factor independence if the individual measurements used in the metric
formulation are independent of each other (Roche 1994). Roche describes factor independence as an
“analytical principle” that applies when a metric is composed of several, individual measurements.
19. Improvement validity: A metric has improvement validity if the metric is an improvement over existing
metrics (El Emam 2000). The term “improvement” that El Emam uses denotes a broad range of possible
improvements that a metric could have. Examples of improvements include ease of measurement, stronger
association with a quality factor, or a closer representation to the attribute being measured.
20. Instrument validity: A metric has instrument validity if the underlying measurement instrument is valid
and properly calibrated (Kitchenham, Pfleeger et al. 1995). For example, consider a tool has been
improperly implemented the definition for branch coverage; this tool, as an instrument, would be invalid.
As a result, the data gathered from that tool (in this case, the poorly defined branch coverage) would also be
considered invalid.
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21. Increasing Growth validity: A metric has increasing growth validity if the metric increases when
concatenating two entities together (Weyuker 1988). Weyuker's Property 9. Said another way, a metric
should never go down if one is concatenating code together. Note that this criterion requires a specific scale
type, which is why Kitchenham et al. explicitly reject this criterion. For example, the code coverage for
different program bodies should never decrease by concatenating two components together.
22. Interaction Sensitivity: A metric has interaction sensitivity if two components of a program result in
different measures depending on how they interact with one another (Weyuker 1988). Weyuker's Property
6. uses this criterion to discuss how components interact with one another, which can be specific to
complexity, but might be a property that applies to other software metrics. For example, cyclomatic number
is not concatenation sensitive as the cyclomatic number of a concatenation of program bodies is always
equal to the sum of the individual cyclomatic numbers of each body. In other words, cyclomatic number
does not take into account the interaction between components, only individual components. The term
“concatenation sensitive” is not used explicitly by Weyuker, but is our interpretation based on the author's
mathematical definition.
23. Internal consistency: A metric has internal consistency if "all of the elementary measurements of a metric
are assessing the same construct and are inter-related" (Curtis 1980). Curtis also argues that a lack of
internal consistency results in losing the ability to interpret the metric. For example, combining the idea of
code complexity and the idea of code churn into a composite metric is not internally consistent because the
notions of complexity and churn are not directly conceptually related.
24. Internal validity: A metric has internal validity if the metric correctly measures the attribute it purports to
measure (El Emam 2000) (Baker, Bieman et al. 1990). Internal validity is a broad category of validation
criteria that is solely concerned with the metric itself, regardless of being associated with an external quality
factor. Most authors of our sources discuss some form of internal validity, however, many will use the term
"theoretical" synonymously with "internal". For a deeper discussion on this issue, see Section 5.1.
25. Monotonicity: A metric has monotonicity if the components of a program are no more complex than the
entire program (Weyuker 1988). Weyuker's Property 5. For example, if a module has one highly complex
method, then the entire module should be at least as complex as that method. This notion applies to other
metrics as well, not just complexity metrics.
26. Metric Reliability: A metric has reliability if the measurements are "accurate and repeatable" (Curtis
1980). Curtis argues that a "reliable" metric ought have little random error, regardless of how the metric is
implemented. For example, cyclomatic complexity is a more reliable measure than psychological
complexity because cyclomatic complexity is deterministically defined, whereas psychological complexity
can only be evaluated through human perception.
27. Non-collinearity: A metric has non-collinearity if it is still correlated with an external quality factor after
controlling for confounding factors (El Emam 2000). For example, if a complexity metric was highly
influenced by code size to the point where no extra variance is explained once code size was included, then
the complexity metric is collinear (and therefore does not pass this criterion).
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28. Non-exploitability: A metric exhibits non-exploitability if developers cannot manipulate a metric to obtain
desired results (Cavano and McCall 1978). We introduce use the term “exploitability” to describe the
phenomenon where people can manipulate a metric's measurements without changing the attribute being
measured. For example, if LOC is being used as an effort metric, then a developer could start writing
exceedingly verbose code to look more productive. Cavano uses the term “stability” when referring to non-
exploitability, which is not to be confused with other authors’ use of stability (#41).
29. Non-uniformity: A metric has non-uniformity if it can produce different values for at least two different
entities (Weyuker 1988). Weyuker's Property 1. As Weyuker states, "A metric which rates all programs as
equal is not really a measure".
30. Notation validity: A metric has notation validity if the metric is reasoned about "mathematically with
precise, consistent notation" (Henderson-Sellers 1996). Henderson-Sellers argues that a metric cannot be
validated by other researchers if the metric is not properly defined with correct, consistent, and
unambiguous mathematical notation. Furthermore, a metric with an unclear definition could mislead other
researchers to draw wrong conclusions about a metric.
31. Permutation validity: A metric has permutation validity if the metric values are responsive to the order of
the statements. (Weyuker 1988). Weyuker's Property 7. Her argument is that the interaction of statements in
a program affects the notion of complexity, so permuting the statements in a program ought to affect the
complexity of a program.
32. Predictability: A metric has predictability if it can be shown to predict values of an external quality factor
with an acceptable level of accuracy (Fenton 1994), (Fenton and Kitchenham 1991), (Schneidewind 1991),
(Schneidewind 1992), (Curtis 1980), (Roche 1994), (Bush and Fenton 1990), (El Emam 2000). Most of the
authors in our sources allude to some form of prediction as one way to validate a metric with an external
quality factor. In each discussion, the authors indicate that showing a metric to be predictive implies that,
historically, a metric could have been used to accurately assess quality in the system. The "acceptable" level
of accuracy would change from process to process and must be interpreted according to the domain of
interest. Note that the Fenton and Schneidewind specifically differentiate predictability from association
(#5).
33. Prediction System validity: A metric has prediction system validity if the metric is part of a model with
procedures on how to use the model, which both must be specified before the study takes place (Baker,
Bieman et al. 1990), (Fenton and Kitchenham 1991), (El Emam 2000). The authors define a prediction
system as involving "a mathematical model and prediction procedures for it". A prediction system has
metrics in addition to models, and a prediction system can be validated. However, the authors emphatically
stress that a metric does not always need to be part of a prediction system to be validated. Showing that a
metric has predictability (#32) does not necessarily show that it can be useful for predicting on the dataset
for any project, only that is has been shown to be useful for prediction in at least one project.
34. Process or Product Relevance: A metric has product or process relevance if it can be “tailored to specific
products or processes” (Roche 1994), (Briand, Emam et al. 1996), (Schneidewind 1991), (Schneidewind
1992). Roche argues that metrics validated in one domain ought to be transferable to other domains.
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35. Protocol validity: A metric has protocol validity if it is measured by a widely accepted measurement
protocol (Kitchenham, Pfleeger et al. 1995). The example that Kitchenham et al. provides is measuring a
person's height: the agreed-upon protocol is from the feet to the head, and not including an upstretched arm.
36. Rank Consistency: A metric has rank consistency if it shares the same ranking as a quality factor
(Schneidewind 1991), (Schneidewind 1992). For example, if code churn were to have rank consistency with
number of faults, then the ranking of files by code churn would match the ranking of files by number of
faults. The rank consistency validation criterion is meant for direct relationships.
37. Renaming Insensitivity: A metric has renaming insensitivity if renaming parts of a program does not
affect the metric's measurement (Weyuker 1988). Weyuker's Property 8. For example, if one were to
rename all of the variables in a program, the complexity value should not change. Although Weyuker
specified this property for complexity, the metric can be generalized to other metrics.
38. Repeatability: A metric has repeatability if the metric is shown to be empirically valid for multiple different
projects or throughout the lifetime of one project (Schneidewind 1991), (Schneidewind 1992), (El Emam
2000) Schneidewind defines the repeatability criterion so that one cannot make a claim of validation on
simply one or two project case studies. While Schneidewind does not provide a concrete number, he implies
that the number of projects required to obtain repeatability might differ from person to person depending on
what they use the metric for. El Emam states "only when evidence has accumulated that a particular metric
is valid across systems and across organizations can we draw general conclusions."
39. Representation condition: A metric satisfies the representation condition if the attribute is a numerical
characterization that preserves properties of both the attribute and the number system it maps to. (Fenton
and Kitchenham 1991), (Kitchenham, Pfleeger et al. 1995), (Fenton 1994), (Bush and Fenton 1990),
(Harman and Clark 2004), (Baker, Bieman et al. 1990). Under the representation condition, any property of
the number system must appropriately map to a property of the attribute being measured (and vice versa).
Fenton (Fenton 1994) describes the representation condition as a two-way correspondence between a metric
and an attribute. Kitchenham (Kitchenham, Pfleeger et al. 1995) states that "intuitive understanding" of an
attribute is preserved when mapping to a numerical system. All of the authors cite the representation
condition from Measurement Theory, a scientific discipline not specific to software engineering.
40. Scale validity: A metric has scale validity if it is defined on an explicit, appropriate scale such that all
meaningful transformations of the metric are admissible (Briand, Emam et al. 1996), (Fenton and
Kitchenham 1991), (Kitchenham, Pfleeger et al. 1995), (Fenton 1994), (El Emam 2000). The scales
discussed are typically: nominal, ordinal, interval, ratio, and absolute. Each scale type denotes a specific set
of transformations that dictate how the metric can be used. As one example, adding two values of a metric
of nominal scale "Yes/No" is not admissible. As another example, the temperature Fahrenheit is of interval
scale which has subtraction as an admissible transformation, meaning that the difference in temperature
between 50 to 60 degrees and 60 to 70 degree are the same. Ratios, however, are not admissible on the
interval scale, meaning that 50 degrees is not twice as hot as 25 degrees. Many of the sources also denote
specific statistical tests that ought to be run in validating metrics of different scale types.
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41. Stability: A metric has stability if it produces the same values "on repeated collections of data under
similar circumstances" (El Emam 2000), (Curtis 1980), (Cavano and McCall 1978). One example of a
metric that might not be fully stable is the number of failures in a system. Since the existence of a failure is
ultimately a decision made by humans (especially in the case of validation failures), two humans may
disagree on whether specific system behavior is a failure or not due to an ambiguous requirements
specification. Cavano calls this “fidelity”.
42. Theoretical validity: A metric has theoretical validity if it does not violate any necessary properties of the
attribute being measured (Kitchenham, Pfleeger et al. 1995), (Briand, Emam et al. 1996), (Briand, Emam et
al. 1995). Theoretical validity is a broad category of validation criteria that involve making arguments about
the properties of a metric. Theoretical validation is usually performed using formal logic. Many authors use
the term “theoretical” synonymous with “internal” validity (#24), however we differentiate the two. For a
deeper discussion on this issue, see Section 5.1.
43. Trackability: A metric has trackability if the metric changes as the external quality factor changes over
time (Schneidewind 1991), (Schneidewind 1992). Schneidewind discusses using trackability to assess
whether a component is improving, degrading, or stagnating in quality over time. In his words, the metric
should “change in unison” with the external quality factor. Interestingly, according to Schneidewind’s
definition, the metric should reflect the external quality factor in such a way that if the external quality
factor changes, then the metric also changes in the same direction. For example, if a high cyclomatic
number is shown to be trackable with the number of faults, then reducing the number of faults in a program
(e.g. fixing the faults) should, in turn, reduce the complexity.
44. Transformation Invariance. A metric has transformation invariance if it results in the same measurement
for two semantically-equivalent programs (Harman and Clark 2004). We use the term "semantically
equivalent" to mean that a compiler could potentially interpret two syntactically-different programs as the
same. Harman et al. claim that if one were to make semantics-preserving changes to a program, then the
value of the metric should not change. Weyuker's Renaming Insensitivity (#36) is one special case of
semantic equivalence. However, two different implementations with indistinguishable results are not
necessarily semantically equivalent. Note that the term “transformation” here is not to be confused with the
admissible transformations mentioned in scale validity (#38); admissible transformations are
transformations of numbers, and this criterion refers to transforming a program.
45. Underlying theory validity: A metric has underlying theory validity if its construction is based upon an
underlying theory that has validity within the domain of the application (El Emam 2000), (Roche 1994),
(Kitchenham, Pfleeger et al. 1995), (Baker, Bieman et al. 1990). To consider a metric to be valid, there
must be a valid theory that describes how the metric measures what it is supposed to measure. For example,
the underlying theory behind code churn is that if code has been shown to change substantially in the
version control system, then the project itself has undergone a substantial amount of change. We note here
that underlying theory validity applies to both internal and external validity; but the difference in these
cases is in how the theory is used. On the internal side, the underlying theory required for validity must
state why the metric in question is worth measuring or why the metric is an accurate representation of the
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attribute being measured from a theoretical standpoint. On the external side, the underlying theory is why a
metric would be statistically associated with an external software quality factor (or external attribute).
46. Unit validity: A metric has unit validity if the units used are an appropriate means of measuring the
attribute (Kitchenham, Pfleeger et al. 1995), (Fenton 1994). For example, fault rate may be used to
measure program correctness or test case effectiveness (Kitchenham, Pfleeger et al. 1995).
47. Usability: A metric has usability if it can be cost-effectively implemented in a quality assurance program
(Cavano and McCall 1978). A metric must be feasibly collected within a process. For example, a metric
that requires several months of computation might not be considered usable.
5. Mapping the Validation Criteria
The list of criteria we present in Section 4 is useful as a reference, but fully understanding the criteria involves
looking at their interrelationships, similarities and differences. Some criteria involve statistics, and some criteria
involve proof of logic arguments. Some criteria involve quality factors, and others do not. Some criteria
constitute parts of other criteria. In this section, we describe how we mapped our criteria into a categorization
scheme.
Our approach to mapping the validation criteria was a bottom-up process. Whenever we found criteria with
similarities, we grouped the criteria together. In other cases, we noticed that some validation criteria are not
atomic, but instead broad categories that can contain many other criteria. For example, internal validity (#24)
cannot be atomically defined because assessing that a metric correctly measures the attribute it purports to
measure is a notion that includes many criteria. Whenever we determined that one criterion was a specific
instance of a separate, broader criterion, we marked the broad criterion as a category.
In the mapping process, we found that all of our criteria groupings could be described by categories we had
already discovered. Thus, we did not introduce new categories of validation criteria, we used only the categories
referred to in the literature in our mapping process.
The result of our mapping process was a categorization of the 47 criteria, as presented in Figure 4. An arrow
between a criterion and a category indicates that the criterion is a part of or specific instance of that group (i.e.
an “is a” relationship). Specific criteria are represented as boxes, categories of criteria are represented as ovals.
The number in parentheses refers to the number of references that directly discussed the criterion.
Our mapping represents the validation criteria and categories we found in the literature. We do not view this
mapping to be a complete list of all possible criteria. Validating a metric by all the leaves of a super category of
criteria does not always imply that the super category is validated. Thus, in any given category, a criterion may
be presented in the future. For example, (shown in Figure 4) attribute validity may not be the only kind of
empirical, internal validity, but is the only kind we have come across in our review. Additionally, empirical
(#16) and theoretical (#42) required multiple categorizations that are described in detail in Section 5.1.
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Figure 4: The 47 criteria, categorized with number of references in parentheses
In the following sections, we describe our reasoning behind some of the major decisions we made in the
mapping process.
5.1 Internal/External vs. Theoretical/Empirical
Beneath our top-level categories are theoretical validity (#42), and empirical validity (#16). While some authors
equate the terms "internal" with "theoretical" and "empirical" with "external" (El Emam 2000) (Baker, Bieman
22
et al. 1990), we distinguish the ideas. We view internal and external validation as dealing with what is being
validated, while theoretical and empirical validation deal with how a metric is validated. Specifically, internal
validation deals with how well a metric measures an attribute, whereas as external validation relates a metric to
a quality factor (i.e., another metric). Theoretical validation uses logic to argue formally whether a metric is
valid or not, while empirical validation employs analysis of data from experimentation or observation. Several
authors equate the terms because, as we have seen in our review, researchers typically perform internal
validation theoretically and external validation empirically. One exception, however, is attribute validity (#6),
which is an empirical way to validate a metric internally.
The notion of an underlying theory (#45) appears in both the external, empirical and internal, theoretical
categories. In each situation, the actual theory would be different. An underlying theory for internal validation
would be about how a metric measures a given attribute, whereas the underlying theory in external validation
would be about how one attribute relates to another attribute.
5.2 Construct Validity
Construct validity (#10) differs from internal and external in that it deals with how a metric is implemented and
studied (i.e. the construct itself). The construct validity of a metric will differ from research project to research
project. For example, one could have a metric that was internally valid and was externally valid, but the analysis
may be wrong because of an incorrectly implemented algorithm (#20).
Definition validity (#12) provides strong motivation for a separate category from internal (#24) and external
(#17) validity. Definition validity deals with providing a clear, unambiguous, deterministically-defined metric.
Many authors (Lincke and Lowe 2006), (Henderson-Sellers 1996), (Baker, Bieman et al. 1990), (El Emam
2000), (Roche 1994) stress the importance of providing clear definitions for both the metrics and the analysis in
metrics validation. Providing a valid metric definition (e.g. in a publication) allows that metric to be correctly
reproduced so that it can be correctly studied and used by other researchers.
5.3 Representation Condition and Internal, Theoretical Validity
The representation condition (#39) is a mathematical property taken from Measurement Theory that deals with
the relationship between a metric's attribute and the number system it maps to. Some authors (Fenton 1994),
(Kitchenham, Pfleeger et al. 1995), (Baker, Bieman et al. 1990) claim that satisfying the representation
condition is the same as internal, theoretical validity. However, we found several criteria that are not concerned
directly with representation condition, but are internal and theoretical. For example, actionability (#2) can be
satisfied by making a logical argument about the attribute being measured, but does not deal with the
mathematical mapping between an attribute and the number system.
5.4 Prediction, Causation, and External Validity
The external, empirical validity category included all of the criteria that involved some sort of statistical analysis
with a quality factor. Some of the authors (Baker, Bieman et al. 1990), (Fenton 1994), (Schneidewind 1992)
point out that external, empirical validation is not made up entirely of prediction. Of Schneidewind's six
23
validation criteria (Schneidewind 1992) (all of which fall into external, empirical), the notion of prediction is its
own category (#30).
Schneidewind's trackability validation criterion (#43) is another example of an external criterion not related to
prediction. Trackability bears closest resemblance to causal relationship validity (#8). Trackability states that a
metric must change as the external quality factor changes. If a metric's attribute truly causes change in
software’s external quality, then trackability ought to be empirically supported (e.g. increasing quality reduces
code size, and vice versa).
6. Spectrum of Philosophies
We postulate that the reason researchers have yet to determine a sufficient set of criteria comes from a
fundamental difference in philosophies about how a metric ought to be used. A metric could be used either as a
pragmatic way of improving software and its surrounding processes or more rigorously as a window into
understanding the very nature of software. We view the differing perspectives as being based on two opposing
philosophies:
The goal-driven philosophy holds that the primary purpose of a metric is to use it in assessment, prediction,
and improvement. Validating a metric internally (#24), then, only serves to improve the usefulness of the
metric in its application. If a metric is “almost” internally valid (i.e. passes many internal validation criteria,
but fails a few), those with a goal-driven perspective would not see a major problem as long as the project
benefited from the guidance and decision support gleaned from using the metric.
The theory-driven philosophy views that the primary purpose of a metric is to gain understanding of the
nature of software. Validating a metric internally, then, is of central importance. If a metric does not follow
the representation condition (#39), for example, then the metric is invalid and should not be further studied.
Those of the theory-driven perspective often denounce the use of external, empirical studies claiming that
the studies do not include a thorough discussion of internal, theoretical validity.
6.1 Goal-Driven Philosophy Principles
More specifically, the goal-driven philosophy can be characterized by the following ideals:
• Specify measurement goals. Metrics should be gathered, defined and analyzed with respect to a specific
goal; that is, how to fix a given set of problems in a given project or organization. For example, Fenton
(Fenton 1994) and Briand et al. (Briand, Emam et al. 1995), explain that measurement activities must
always have clear objectives and in fact be objective-based (e.g. goal/question/metric (Basili and Weiss
1994)) also agree with this idea.
• Goals vary with specific processes and products. Metrics can only be validated to a certain project,
process, or environment. Schneidewind (Schneidewind 1991) and Roche (Roche 1994) contend that metrics
should be used in similar processes, products or environments.
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• Validation is a continuous process. Since metrics are validated to specific projects, a metric that is valid
today may not be valid tomorrow (even on the same project), and a metric that is valid on the current
project may not be relevant on another project. For example, Schneidewind explains that the fundamental
problem in software metrics validation is the following: there must be a project in which metrics are
validated, and a different project in which the metrics are applied. A project could suffer from significant
time lags, product differences, and process differences, and these scheduling differences should signal the
need to exercise care in choosing the two projects such that the application of the metrics is appropriate
(Schneidewind 1991).
• All theoretical analysis eventually serves a goal. Theoretical analysis, such as the representation
condition, ought to be pursued, but only insofar as helping achieve the measurement goal. For example,
Schneidewind explains that the purpose of metrics validation is to identify metrics that are related to
software quality factors (which are typically the measurement goal) (Schneidewind 1991).
• Metrics can have an ad-hoc definition. A metric can be specific to a product, process, environment, or
technology. For example, a metric that looks for the use of a specific module in the code would be an ad
hoc definition as it would not have meaning outside of its project. Those of the goal-driven perspective
would view ad hoc definitions acceptable as long as the metric leads to fulfilling a goal (Schneidewind
1991).
• Actionable metrics are the best. Actionable metrics that are associated with quality factors are the most
desirable as they can be used to predict and improve the process. Un-actionable prediction is less useful, but
can still fulfill specific goals and should still be pursued (Fenton and Neil 2000), (Roche 1994).
• “Good enough” is good enough. Statistical theory is only relevant to the extent that it helps us to measure
the association or predictability of an actionable metric. To the goal-driven, a debate on whether a metric is
defined over the correct scale type is less important than external validation because an improper scale type
can still be used in practice and achieve effective results (Cavano and McCall 1978), (Jones 1994).
• No universally applicable set of criteria exists. All validation criteria serve to fulfill a specific goal, which
can vary from project to project. The goal, then dictates which criteria apply to a given project.
6.2 Theory-Driven Philosophy Principles
The theory-driven philosophy can be characterized by the following ideals:
• Must have a theory. Metrics should be gathered based upon an underlying theory of how the measurement
is representative of an attribute in the software. Improvement in a process-driven sense takes a back seat to
improvement of our knowledge of software. For example, Briand, et al. (Briand, Emam et al. 1996) contend
that internal attributes are interesting for software engineers as long as they are a part of software
engineering theories.
• Metrics should be generally applicable. A metric must be universally defined before we can begin to
apply it. For example, Lincke (Lincke and Lowe 2006) contends that metric definitions should be
independent of environments or project-specifics.
25
• Metrics should be repeatable. Metrics should be gathered systematically by a program or clearly specified
procedure, so as to ensure that there are no errors during measurement. The goal-driven philosophy would
agree with this idea, too, but only to the extent that the error is within an acceptable range to make an
acceptable prediction (Schneidewind 1991).
• Theoretical, internal validation is paramount. All possible values of the metric must align with the
assumptions of the attribute being measured. Insinuated in this idea is that a metric should be held to close
scrutiny mathematically and analytically before it is ever tested empirically or applied to a process. Scale
type, admissible transformations, and appropriate use of statistical techniques are all stressed (Kitchenham,
Pfleeger et al. 1995), (Briand, Emam et al. 1996), (Briand, Emam et al. 1995).
• Know the underlying reasons. Eventually, the true validation of metrics can help us understand the
underlying forces that cause software and the software development process to behave the way that they do
(El Emam 2000), (Roche 1994), (Kitchenham, Pfleeger et al. 1995), (Baker, Bieman et al. 1990).
• Un-actionable is not useless. Just because a metric is not actionable does not render it useless to
understanding software. Some metrics are relevant because they help us characterize software for many
purposes outside of prediction and other specific project goals. Therefore, those of theory-driven
philosophy would view actionability as orthogonal to a metric’s validity (Kitchenham, Pfleeger et al. 1995),
(Briand, Emam et al. 1996), (Briand, Emam et al. 1995).
• A universally applicable set of criteria does exist. A universally-applicable set of criteria must exist if we
are to understand and agree upon the nature of software.
We contend that the two ends of the spectrum are counter-opposed, meaning they compete with one another
both in theory and in practice. However, the two philosophies are not mutually exclusive. A given researcher or
practitioner may agree or disagree with some aspects of both extremes and borrow motivations from both
philosophies. Even within the same sources, we frequently discovered metrics validation criteria that seemed to
emanate from both philosophies. As such, we contend that the two philosophies below represent the two ends of
a spectrum.
At first glance, one may think that all practitioners are goal-driven and all researchers are theory-driven,
however, we do not consider this to be the case. For example, a developer can be theory-driven because she
wants a complexity metric to represent what she believes is complex code. Conversely, a researcher can be goal-
driven because he cares more about the applicability of his research than being theoretically correct. Therefore,
researchers and practitioners can be at any point along the spectrum.
In terms of the criteria motivation, one may consider a relative ordering of a given validation criterion or set of
criteria in terms of their position on the spectrum, but we find that no objective system of measurement exists
for determining such an ordering. Thus, we do not indicate a mapping of the criteria onto the spectrum we
propose in this paper. We do not view that one paper, author, or criterion fully adhere to one extreme or the
other. However, we view the following as representative examples of criteria that are motivated by either the
goal-driven philosophy or the theory-driven philosophy.
26
• We view five of Schneidewind's six criteria (Schneidewind 1991), (Schneidewind 1992) to be primarily
motivated by a goal-driven philosophy: association (#5), rank consistency (#36), discriminative power,
(#13), predictability (#30), and trackability (#42).
• However, we view Schneidewind's sixth criterion, repeatability (#35), as being in the middle of the
spectrum. If a metric has been shown to be related to a quality factor on repeated occasions, then it is
reliable for satisfying specific project goals and lends credence to a universal truth.
• We view the representation condition (#39) and its sub-criteria to be primarily motivated by a theory-driven
philosophy. If a metric satisfies the representation condition, then understanding the number system the
metric maps to implies understanding the attribute being measured.
• We view actionability (#2) to be primarily motivated by the goal-driven philosophy. Actionability is often
discussed in terms of satisfying specific goals of a project (Curtis 1980), (Roche 1994), (Fenton and Neil
2000). Those of the theory-driven philosophy would view actionability as orthogonal to a metric's validity:
if a metric is valid but is un-actionable in practice, it still speaks to the nature of software. The same
argument applies to many of the criteria that involve utility, such as economic productivity (#15) and
product or process relevance (#34).
7. Choosing Appropriate Metrics Validation Criteria
In Section 6, we described how the theory-driven and goal-driven perspectives are diametrically opposed,
leading to a conflict in how the community agrees upon how a metric ought be validated. In this section, we
provide some guidance on the use of the criteria to make the information in this paper more actionable. Many of
the tenets of each philosophy are based upon the intended use of a metric. For example, in the theory-driven
perspective, intended uses of a metric involve discovering the nature of software, whereas the goal-driven
perspective typically uses metrics to satisfy business goals.
One of the objectives of this review is to reveal how the software engineering community believes a metric is to
be considered valid, that is, suitable and acceptable for its intended use. Introducing the intended use along with
the metric, therefore, is a critical step toward metric validation. A metric that is valid for one intended use may
not be valid for another intended use. For example, a metric could be useful for demonstrating universal theories
about software, but also be infeasible to collect and apply in a development process. In such a case, the metric
would be considered valid for the former use, and invalid for the latter use.
Deciding on a particular intended use points the researcher toward specific properties of a metric that are more
appropriate for that use; we call these advantages. For example, showing the metric to be a meaningful
representation of the attribute is one advantage (see “Meaningfulness” below), and showing that it can be
applied to a development process is another advantage (see “Practicality” below). Furthermore, showing that a
metric lacks an advantage can be a way to articulate a metric’s limitation. To demonstrate that a metric has
specific advantages, a researcher or practitioner needs use the criteria that provide those advantages.
In this review, we observed 11 common advantages from the 47 criteria. Each advantage is an abstract property
of a metric that a researcher could demonstrate using its associated validation criteria. In Section 7.1, we
27
describe the 11 advantages and map them to the criteria. In Section 7.2, we propose a step-by-step process of
applying the validation criteria via the intended use, advantages, and the information found in previous sections
of this paper.
7.1 Observed Advantages of Using Various Metrics Validation Criteria
The following is a list of the advantages for metrics validation criteria that we have observed in the sources for
this survey. The first and second authors of this paper examined the list of criteria to articulate the advantages of
each metric validation criterion. We then synthesized our findings and collaboratively developed this list,
maintaining traceability from the advantages to the criteria. We do not claim that these are the only advantages
of metrics that could be demonstrated. Table 6 provides our mapping from the advantages to the criteria
themselves.
• Mathematical Soundness. Enables users of the metric to safely perform specified mathematical
operations on the metric without the concern that the results will misrepresent the attribute.
• Practicality. Software engineers can directly apply the metric to improve their software development
processes and practices. Criteria that give the practicality advantage show that a metric can be feasibly
deployed in a software development setting.
• Correctness. The implementation of a metric rarely obtains incorrect values, which applies especially
to construct validity types of criteria.
• Efficiency. The efficiency advantage allows practitioners and researchers to save time and energy by
choosing a single metric for a given measurement goal.
• Difference-detecting. The difference-detecting advantage enables metrics to carefully detect
differences in the attribute, while avoiding metrics that are too dependent on the measured attribute.
• Hypothesis-strengthening. Empirical work gives researchers more confidence in the conclusions
because of repeated observations. The hypothesis-strengthening advantage also increases researchers’
confidence in the theory being presented.
• Meaningfulness. The meaningfulness advantage implies an intuitive, easy to understand, conceptual
relationship between the metric and the attribute that ensures the interpretability of the metric. Do
researchers intuitively know what the metric means?
• Decision-informing. The metric helps researchers and practitioners make informed decisions while
developing software. For example, association may indicate that a factor is related to quality, but if the
metric is unactionable it still may help with risk assessment. Criteria that provide the decision-
informing advantage focus research on a metric, regardless of how well it represents its attribute.
• Quality-focused. Criteria that provide the quality-focused advantage indicate that a metric is useful for
improving the peoples’ lives through high quality software.
• Theory-building. The theory-building advantage enables researchers or practitioners to make general
statements about the nature of software and its development.
28
• Consensus Contribution. The consensus contribution advantage highlights criteria that add to the
common understanding of a metric’s underlying attribute. This advantage also helps researchers agree
how they define the underlying attribute, which in turn helps define the metric better. Does everybody
understand how to collect and interpret the metric in the same way?
Table 6. Mapping from Criteria to Advantages
# Criterion Mat
hem
atic
al S
ound
ness
Prac
tical
ity
Cor
rect
ness
Eff
icie
ncy
Hyp
othe
sis-
stre
ngth
enin
g
Mea
ning
fuln
ess
Dec
isio
n-in
form
ing
Qua
lity-
focu
sed
The
ory-
build
ing
Con
sens
us C
ontr
ibut
ion
Diff
eren
ce-d
etec
ting
1 A Priori Validity X
2 Actionability X X
3 Appropriate Continuity X X X
4 Appropriate Granularity X
5 Association X X
6 Attribute Validity X X
7 Causal Model Validity X X X
8 Causal Relationship Validity X X X
9 Content Validity X X
10 Construct Validity X X
11 Constructiveness X X
12 Definition Validity X
13 Discriminative Power X X X
14 Dimensional Consistency X X
15 Economic Productivity X X
16 Empirical Validity X X
17 External Validity X X X
18 Factor Independence X X
19 Improvement Validity X
20 Instrument Validity X X
21 Increasing Growth Validity X X
22 Interaction Sensitivity X X
23 Internal Consistency X
24 Internal Validity X
25 Monotonicity X
29
# Criterion Mat
hem
atic
al S
ound
ness
Prac
tical
ity
Cor
rect
ness
Eff
icie
ncy
Hyp
othe
sis-
stre
ngth
enin
g
Mea
ning
fuln
ess
Dec
isio
n-in
form
ing
Qua
lity-
focu
sed
The
ory-
build
ing
Con
sens
us C
ontr
ibut
ion
Diff
eren
ce-d
etec
ting
26 Metric Reliability X
27 Non-collinearity X X
28 Non-exploitability X
29 Non-uniformity X X X
30 Notation Validity X X
31 Permutation Validity X
32 Predictability X X X
33 Prediction System Validity X X X
34 Product or Process Relevance X
35 Protocol Validity X X
36 Rank Consistency X X X
37 Renaming Insensitivity X
38 Repeatability X X
39 Representation Condition X X
40 Scale Validity X
41 Stability X X
42 Theoretical Validity X
43 Trackability X X
44 Transformation Invariance X
45 Underlying Theory Validity X
46 Unit Validity X
47 Usability X X X
7.2 Criteria Application Process
To choose the appropriate metrics validation criteria for a specific metric, a researcher could perform the
following six steps in order. Note that this methodology does not guarantee that a metric is valid for its intended
use. Instead, this process acts as a guide for using the current state of the literature to demonstrate the
advantages and limitations of a metric. Ultimately, a researcher who intends to validate a metric must consult
the literature for a thorough analysis of that metric’s validity.
1. Determine the intended use of the metric. The researcher validating the metric examines how the metric
ought to be used. Metrics’ intended uses are numerous and vary according to specific practical or scientific
contexts.
30
2. Using Table 6, highlight the advantages that are appropriate for the intended use chosen in Step 1.
Researchers can decide on the advantages that they wish to present to the research community or to a
software development team.
3. Look up the validation criteria that are tied to the advantages using Table 6.
4. Carefully choose validation criteria from the list provided by Table 6 while considering the intended use,
relationships, and motivations in the community amongst the applicable criteria, found in Sections 5 and 6.
Do not choose criteria based upon how well a metric performs, but rather only by the appropriateness of the
criterion to the intended use.
5. Demonstrate that the metric does or does not follow the chosen validation criteria.
6. In presenting the metric in academic publication, use the vocabulary of Table 6 and Section 4 to describe
the advantages and limitations of the metric in the context of the intended use identified in Step 1.
For a detailed example, suppose a researcher is proposing the metric YearsExperience: YearsExperience
is equal to the sum of the number of years of software development experience on all of the members of the
team. Following the steps above,
1. The researcher determines the intended use of YearsExperience as evaluating the team’s ability to
develop high-quality software.
2. In proposing this metric to the community, the researcher highlights the advantage that
YearsExperience will save time and money when applied to a process (i.e. the “Efficiency” advantage
described above).
3. The researcher looks up the Efficiency advantage, and discovers that it maps to Improvement Validity
(#19) and Usabilty (#47) in Table 6.
4. Both validity criteria apply to the intended use. Thus, to highlight the efficiency of YearsExperience, the
researcher would choose these two validation criteria.
5. The researcher then (a) examines other team metrics and demonstrate that YearsExperience is an
improvement over current metrics (#19) and (b) demonstrates that YearsExperience can be applied to a
software development process (#47).
6. In presenting the metric’s validation, either to the team or to the academic community, the researcher then
uses the vocabulary of Table 6 (i.e. indicate that it is more efficient) to describe the metrics’ advantages
and limitations. Incidentally, the Usability criterion also has the advantage of Practicality and being
Quality-Focused, two points that can also be argued in the researcher’s work.
8. Conclusion
Our systematic literature review revealed that the academic literature contains a highly diverse set of assertions
on what constitutes a valid metric. Our review resulted in 47 distinct validation criteria in the published software
engineering literature, coming from 20 papers and 20 distinct authors. Some of the authors explicitly disagree
31
with some criteria, while other criteria subsume each other. Researchers proposing new metrics should consider
the applicability of the validation criteria in terms the intended use and the advantages described in this paper.
Understanding the opposing motivations behind the criteria helps us take the next steps toward establishing
context-specific sets of validation criteria that are widely accepted. Considering validation criteria with respect
to metrics’ intended uses can bring metrics validation research from ad hoc analysis to a mature science of
measurement and software improvement.
9. References
Baker, A. L., J. M. Bieman, N. Fenton, D. Gustafson, A. Melton and R. Whitty (1990). "A philosophy for software measurement." Journal of Systems and Software 12(3): 277-281.
Basili, V. R. and Weiss (1994). "A methodology for collecting valid software engineering data." IEEE Transactions on Software Engineering SE-IO(6): 728-738.
Brereton, P., B. A. Kitchenham, D. Budgen, M. Turner and M. Khalil (2007). "Lessons from Applying the Systematic Literature Review Process Within the Software Engineering Domain." Journal of Systems and Software 80: 571-583.
Briand, L., K. E. Emam and S. Morasca (1995). Theoretical and empirical validation of software product measures, International Software Engineering Research Network, Technical Report, #ISERN-95-04.
Briand, L. C., K. E. Emam and S. Morasca (1996). "On the Application of Measurement Theory in Software Engineering." Empirical Software Engineering 1(1): 61-88.
Bush, M. E. and N. E. Fenton (1990). "Software measurement: A conceptual framework." Journal of Systems and Software 12(3): 223-231.
Cavano, J. and J. McCall (1978). A framework for the measurement of software quality. Software quality assurance workshop on functional and performance issues.
Courtney, R. E. and D. A. Gustafson (1993). "Shotgun Correlations in Software Measures." Software Engineering Journal 8(1): 5-13.
Curtis, B. (1980). "Measurement and experimentation in Software Engineering." Proceedings of the IEEE 68(9): 1144-1157.
El Emam, K. (2000). A Methodology for Validating Software Product Metrics, National Research Council of Canada, Ottawa, Ontario, Canada NCR/ERC-1076, June.
Elbaum, S. G. and J. C. Munson (1998). Getting a handle on the fault injection process: validation of measurement tools. Software Metrics Symposium, 1998. Metrics 1998. Proceedings. Fifth International.
Fenton, N. (1994). "Software measurement: a necessary scientific basis." IEEE Transactions on Software Engineering 20(3): 199-206.
Fenton, N. and B. Kitchenham (1991). "Validating software measures." Journal of Software Testing, Verification & Reliability 1(2): 27-42.
Fenton, N. and M. Neil (1999). "Software metrics: successes, failures and new directions." Journal of Systems and Software 47(2-3): 149-157.
Fenton, N. E. and M. Neil (2000). Software metrics: roadmap. Future of Software Engineering, Limerick, Ireland.
Harman, M. and J. Clark (2004). Metrics are fitness functions too. 10th International Symposium on Software Metrics.
Henderson-Sellers, B. (1996). "The mathematical validity of software metrics." ACM SIGSOFT Software Engineering Notes 21(5): 89-94.
IEEE (1990). IEEE Standard 610.12-1990, IEEE Standard Glossary of Software Engineering Terminology.
32
ISO/IEC (1991). "ISO/IEC 9126: Information Technology - Software Product Evaluation - Quality Characteristics and Guidelines for their Use,." International Organization for Standardization and the International Electrotechnical Commission.
Jones, C. (1994). "Software metrics: good, bad and missing." Computer 27(9): 98-100.
Kitchenham, B. (2004). "Procedures for Performing Systematic Reviews." Joint Technical Report, Keele University Technical Report TR/SE-0401 and NICTA Technical Report 0400011T.
Kitchenham, B. (2010). "What's up with software metrics? - A preliminary mapping study." Journal of Systems and Software 83(1): 37-51.
Kitchenham, B., S. L. Pfleeger and N. Fenton (1995). "Towards a Framework for Software Measurement Validation." IEEE Transactions on Software Engineering 21(12): 929-944.
Lincke, R. and W. Lowe (2006). Foundations for defining software metrics. 3rd International Workshop on Metamodels, Schemas, Grammars, and Ontologies for Reverse Engineering (ATEM '06), Genoa, Italy.
McCabe, T. (1976). "A complexity measure." IEEE Transactions on Software Engineering SE-2(4): 308-320.
N. Ayewah, D Hovemeyer, JD Morgenthaler, J. Penix and W. Pugh (2008). "Using Static Analysis to Find Bugs." IEEE Software 25(5): 22-29.
Rao, P. V. (2007). Statistical Research Methods in Life Sciences. Pacific Grove, CA, Duxbury Press.
Roche, J. M. (1994). "Software metrics and measurement principles." ACM SIGSOFT Software Engineering Notes 19(1): 77-85.
Schneidewind, N. F. (1991). Validating software metrics: producing quality discriminators. International Symposium on Software Reliability Engineering.
Schneidewind, N. F. (1992). "Methodology for validating software metrics." IEEE Transactions on Software Engineering 18(5): 410-422.
Weyuker, E. J. (1988). "Evaluating software complexity measures." IEEE Transactions on Software Engineering 14(9): 1357-1365.
